Integrated variable inductor

ABSTRACT

A novel form of an integrated variable inductor uses an on-chip transformer together with a variable capacitor. The variable capacitor can either be a varactor or a switched capacitor array and is connected to the secondary coil of the transformer. By changing the capacitance at the secondary coil of a transformer, the equivalent inductance looking into the primary coil of the transformer can be adjusted. With another capacitor in parallel to the primary coil, two different modes of resonance inherently exist, and a very wide frequency tuning range can be achieved by combining the two modes.

FIELD OF THE INVENTION

The present invention relates generally to variable inductors and, moreparticularly, to an integrated variable inductor using an on-chiptransformer and a variable capacitor.

BACKGROUND OF THE INVENTION

Frequency tuning mechanisms are required in a wide range of differentapplications. For example they are required in wireless transceivers forthe down conversion of signals at different frequencies, formultiple-band applications and for wide band applications. An idealfrequency tuning circuit will have a wide tuning range, be powerefficient and have a high operating frequency.

Conventionally a tuning circuit includes an LC tank, and a conventionalmethod of providing control of the tuning frequency is by using avariable capacitance such as a varactor to vary the value of C in the LCtank. Several classes of varactors, such as junction diodes and MOScapacitors, are commonly found. However, this arrangement has thedisadvantage that there is a limited frequency range (about 10% only)owing to the limited capacitance ratio of the varactor. Also, becausethe power consumption of the LC tank is high, it is more power efficientto minimize the capacitance of the tank and to adjust the inductance forfrequency variation. As a result, it is highly desirable to be able toimplement integrated variable inductors.

Currently, several techniques are available for providing a variableinductance. These include active inductors and switched resonators. Atypical design for an active inductor is the gyrator-C architecture,which employs a gyrator and an integrating capacitor. A gyrator consistsof two transconductors connected in a feedback configuration, as shownin FIG. 1. This type of active inductor makes use of the parasiticcapacitance of the transistors as the integrating capacitor. Theinductance of active inductor is:${Z_{i\quad n}\left( {j\quad\omega} \right)} = \frac{g_{ds1} + {{j\omega}\left( {c_{gs2} + c_{gd1} + c_{gd2}} \right)}}{\left( {g_{m1} + g_{ds1} + {j\quad\omega\quad c_{gd2}}} \right)\left( {g_{m2} + {{j\omega}\left( {c_{gs2} + c_{gd1}} \right)}} \right)}$

Because only a few active devices are used in this type of inductor, thechip area occupied is usually very small. Tunability is anotheradvantage of this type of active inductor. As shown in the aboveequation, by changing the bias and, therefore, the transconductance ofthe transistors, the inductance of the active inductor can be varied.

However, the power consumption and noise contribution of the activedevices used in these inductors are generally too high to be practical,and the dynamic range is quite limited. Most important of all, activeinductors are generally not suitable for high frequency operation. Athigh frequencies, the performance of the active inductor is degraded bythe phase errors induced by parasitics.

Recently, switched resonators using multiple inductors have beenintroduced. A switched resonator typically comprises two spiralinductors and a switching transistor, either connected in parallel or inseries with the inductors as shown in FIG. 2. If the switchingtransistor is connected in parallel with one of the inductors, theinductor is shorted when the switch is on. As a result, the equivalentinductance reduces from L₁+L₂ to L₁.

A switched resonator can be used for coarse tuning and another varactorcan be used for fine tuning. The tuning range of the resonator cantherefore be significantly improved. However, the turn-on resistance ofthe switching transistor has a great impact on the quality factor of theresonator. It is necessary to increase the size of the transistor inorder to reduce the effect of the turn-on resistance on the qualityfactor. Since the operating frequency of the resonator depends on theequivalent inductance and the capacitance between drain and ground ofthe switching transistor, the drain capacitance of the switchsignificantly reduces the operating frequency of the resonator. Thus,this type of switched resonator is not suitable for applications withlow noise, low power, and high frequency.

It is also possible to frequency tune some types of resonators bymechanically changing a property of these resonators. However, this isnot feasible if the resonator is to be integrated on chip.

Thus, it is desirable to provide a variable inductance that is suitablefor high frequency circuits and has reduced power consumption andreduced noise degradation.

SUMMARY OF THE INVENTION

According to the present invention there is provided a variable inductorcomprising a transformer having primary and secondary coils, wherein avariable capacitance is provided in parallel with said secondary coil.By changing the capacitance at the secondary coil of a transformer, theequivalent inductance looking into the primary coil of the transformercan be adjusted.

In exemplary embodiments of the invention, the variable capacitance maybe provided by a varactor or a switched capacitor array, for example.

In another aspect of the present invention, a capacitance is alsoprovided in parallel with the primary coil. With another capacitor inparallel to the primary coil, two different modes of resonanceinherently exist, and a very wide frequency tuning range can be achievedby combining the two modes. This capacitance may be a fixed capacitor orsimply parasitic capacitance of the primary coil in various embodimentsof the invention. In another embodiment, the capacitance in parallelwith the primary coil is a variable capacitance.

In another aspect of the invention, the primary and secondary coils maybe coupled together by a mutual inductance.

In accordance with yet another aspect of the invention, a voltagecontrolled oscillator includes a variable inductor comprising atransformer having primary and secondary coils, wherein a variablecapacitance is provided in parallel to said secondary coil.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments of the invention will now be described by way ofexample and with reference to the accompanying drawings, in which:

FIG. 1 shows a prior art active inductor,

FIG. 2 shows prior art switched resonators,

FIG. 3 shows the impedance of a simple LC resonator with a varying ratioof L and C,

FIG. 4 shows a schematic of a variable inductor according to anembodiment of the invention,

FIG. 5 shows an example of the frequency response of a resonatorconsisting of a variable inductor and a capacitor according to anembodiment of the invention,

FIG. 6 shows a variable inductor using π model,

FIG. 7 shows a T-model representation of a variable inductor,

FIG. 8 shows a resonator with a variable inductor according to anembodiment of the invention,

FIG. 9 shows a T-model representation of a variable inductor accordingto an embodiment of the invention with resistive components,

FIG. 10 shows an example of the inductance against frequency in anembodiment of the invention using the T-model representation of FIG. 9,

FIG. 11 shows a resonator with a variable inductor according to anembodiment of the invention with resistive components,

FIG. 12 shows a graphical representation of Equation (5),

FIG. 13 shows the effective inductance of an embodiment of the presentinvention against C₂,

FIG. 14 shows the curves of FIG. 12 aligned with the corresponding Z₁₁,

FIG. 15 illustrates the switching of the maximum input impedance in anoscillator using an embodiment of the invention,

FIG. 16 shows a schematic of a voltage-controlled oscillator with anembodiment of the present invention,

FIG. 17 shows details of the capacitors C_(2p) and C_(2n) shown in FIG.16,

FIG. 18 shows simulation results of the voltage-controlled oscillator ofthe embodiment of FIG. 16,

FIG. 19 compares the performance of a VCO formed in accordance with anembodiment of the invention with the prior art,

FIG. 20 shows a testing setup using coupled microstrip lines,

FIG. 21 shows the lumped model of the microstrip lines in FIG. 20

FIG. 22 shows the measurement results of the coupled microstrip lines,

FIG. 23 shows a testing setup for obtaining Z₁₁ of circuits according toan embodiment of the invention,

FIG. 24 shows the Smith chart of the measured S₁₁, and

FIG. 25 shows the measured equivalent inductance with different off-chipcapacitors,

FIG. 26 is a die photo of a VCO formed according to an embodiment of theinvention,

FIG. 27 shows the frequency spectrum and phase noise at the output ofthe VCO with the first-mode of oscillation, and

FIG. 28 shows the frequency spectrum and phase noise at the output ofthe VCO with the second-mode of oscillation.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

FIG. 3 shows the impedance of a simple LC resonator when the ratio ofthe L and C is varied and the resonant frequency is kept unchanged. Forsuch an LC oscillator, if the value of L increases, the impedance of thetank also increases. Then, less ac current and, therefore, less dc poweris required to attain the same output amplitude. In other words, inorder to reduce the power consumption, it is advantageous to maximizethe inductance, or, to minimize the capacitance in an LC tank.

Moreover, for an inductor with a series resistance of r_(s), theparallel resistance of the inductor is $\frac{\omega^{2}L^{2}}{r_{s}}.$For an oscillator, in order to start up oscillation, the followingcondition has to be fulfilled, $\frac{G_{m}\omega^{2}L^{2}}{r_{s}} = 1$

Assuming that the quality factor of the inductor remains almost the samefor different frequencies, when L increases, G_(m) decreases and thepower consumption can be reduced.

Conventionally, frequency tuning is achieved by changing the capacitanceof a tank using varactor. However, as mentioned before, it is more powerefficient to minimize the capacitance of the tank and adjust theinductance for frequency variation. Therefore, the need for a variableinductor arises.

FIG. 4 shows the schematic of a variable inductor according to anembodiment of the present invention. In this embodiment the variableinductor comprises a transformer with two capacitors. C₁ is thecapacitor connected to the primary coil and C₂is the other capacitorconnected to the secondary coil. C₁ can either be the parasiticcapacitance, a fixed capacitor, or a varactor, whereas C₂ can be avaractor or a switched capacitor array. By changing the capacitance ofC₂, the equivalent inductance looking into the primary coil of thetransformer can be tuned. FIG. 5 shows an example of the frequencyresponse of a resonator consisting of a variable inductor and a fixedcapacitance.

With this embodiment of the invention there are two modes of frequencytuning: frequency tuning in a single mode, and frequency tuning bymode-switching. Together with its own parasitic capacitance, the primarycoil will resonate at different frequencies, which are determined by thevalue of the capacitance at the secondary coil. By connecting anothervaractor at the primary coil, the frequency tuning range can be furtherextended to be much larger than that can be achieved with existingsolutions with variable capacitors.

It has also been shown by theory, simulation, and experiments that thereexist two different resonant modes associated with the proposed variableinductor. The tuning range of the invention can be greatly increased bycombining two modes. Since the variable inductor of the preferredembodiments only comprises passive components, no power consumption isrequired which is highly advantageous.

In order to explain the two resonant frequencies and the mode-switchingproperty of the transformer intuitively, the π model can be used asshown in FIG. 6.

The two LC tanks with two different resonant frequencies shown in FIG. 6are coupled to each other by the mutual inductance,$\frac{{L_{1}L_{2}} - M^{2}}{M}.$Hence, it can be concluded that two resonant frequencies are inherent ina transformer.

The ideal case is considered first. Lumped components without resistiveloss are used for the analysis here. A T-model, as shown in FIG. 7, isused for the analysis. Its input impedance, Z₁₁, can be calculated asshown below: $\begin{matrix}{Z_{11} = {{s\left( {L_{1} + \frac{\omega^{2}k^{2}L_{1}L_{2}C_{2}}{1 - {\omega^{2}L_{2}C_{2}}}} \right)} = {sL}_{eff}}} & \quad \\{{where}\quad\left\{ \begin{matrix}{L_{eff} = {{L_{1} + \frac{\omega^{2}k^{2}L_{1}L_{2}C_{2}}{1 - {\omega^{2}L_{2}C_{2}}}} = {L_{1} + \frac{\omega^{2}k^{2}L_{1}}{{\omega_{2}}^{2} - \omega^{2}}}}} \\{\omega_{2} = \frac{1}{\sqrt{L_{2}C_{2}}}}\end{matrix} \right.} & (1)\end{matrix}$

Five properties of the variable inductor can be derived from the aboveequation:

-   -   1. When ω→0 or C₂→0, L_(eff)=L₁    -   2. When ω→∞ or C₂→∞, L_(eff)=L₁(1−k²)    -   3. When ω=ω₂, L_(eff)∞    -   4. When ω→ω₂ ⁺, L_(eff)>0    -   5. When ω→ω₂ ⁻, L_(eff)<0

L_(eff) will reach the largest value when ω=ω₂=$\omega = {\omega_{2} = {\frac{1}{\sqrt{L_{2}C_{2}}}.}}$In practice, the largest value of L_(eff) cannot be infinite becausethere is lossy component in the variable inductor, which is not includedhere, but will be revisited in the later analysis.

Thus, it can be concluded that the input impedance of an embodiment ofthe present invention is inductive and can be represented by the aboveequation. By changing the value of C₂, the values of the equivalentinductance can be adjusted accordingly. C₂ can either be a varactor or aswitched capacitor array.

If the variable inductor is connected to a capacitor in parallel, asshown in FIG. 8, a resonator with tunable resonant frequency can beimplemented. The following equations can then be derived from FIG. 8:$\begin{matrix}\left\{ \begin{matrix}{{L_{eff}C_{1}} = \frac{1}{{\omega_{0}}^{2}}} \\{L_{eff} = {L_{1} + \frac{{\omega_{0}}^{2}k^{2}L_{1}L_{2}C_{2}}{1 - {{\omega_{0}}^{2}L_{2}C_{2}}}}}\end{matrix} \right. & \quad \\{{\left. \Rightarrow\omega_{0} \right. = \sqrt{\frac{\left( {{\omega_{1}}^{2} + {\omega_{2}}^{2}} \right) \pm \sqrt{\left( {{\omega_{1}}^{2} - {\omega_{2}}^{2}} \right)^{2} + {4k^{2}{\omega_{1}}^{2}{\omega_{2}}^{2}}}}{2\left( {1 - k^{2}} \right)}}}{{{where}\quad L_{1}C_{1}} = {{\frac{1}{{\omega_{1}}^{2}}\quad{and}\quad L_{2}C_{2}} = \frac{1}{{\omega_{2}}^{2}}}}} & (2)\end{matrix}$

Since (L₁C₁-L₂C₂)²+4k²L₁L₂C₁C₂>0, there are always two resonantfrequencies.

Similarly, the equivalent inductance in the resonator can be derived asshown below, $\begin{matrix}{L_{eff} = \frac{{L_{2}C_{2}} + {{L_{1}C_{1}} \pm \sqrt{\left( {{L_{2}C_{2}} - {L_{1}C_{1}}} \right)^{2} + {4k^{2}L_{1}C_{1}L_{2}C_{2}}}}}{2C_{1}}} & (3)\end{matrix}$

Since (L₁C₁−L₂C₂)²+4k²L₁L₂C₁C₂>0, there are two values of L_(eff), whichcorrespond to the two resonant frequencies derived previously.

Lumped components with resistive loss are used for the further analysis.A T-model, as shown in FIG. 9, is used for the analysis. The inputimpedance, Z₁₁, can be calculated as shown below: $\begin{matrix}{Z_{11} = {r_{eff} + {sL}_{eff}}} & \quad \\{{where}\quad\left\{ \begin{matrix}{r_{eff} = {r_{1} + \frac{\omega^{4}{C_{2}}^{2}r_{2}k^{2}L_{1}L_{2}}{\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)^{2} + {\omega^{2}{C_{2}}^{2}{r_{2}}^{2}}}}} \\\begin{matrix}{L_{eff} = {L_{1} + \frac{{\omega^{2}k^{2}L_{1}L_{2}C_{2}} - {\omega^{4}{C_{2}}^{2}k^{2}L_{1}{L_{2}}^{2}}}{\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)^{2} + {\omega^{2}{C_{2}}^{2}{r_{2}}^{2}}}}} \\{= {L_{1} + \frac{\omega^{2}k^{2}L_{1}L_{2}{C_{2}\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)}}{\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)^{2} + {\omega^{2}{C_{2}}^{2}{r_{2}}^{2}}}}}\end{matrix}\end{matrix} \right.} & (4)\end{matrix}$

FIG. 10 shows an example of the variable inductance against frequencyusing the model with resistive components. There are three regions ofoperation. Two of them are inductive and one of them is capacitive. Touse the present embodiment of the invention as a variable inductor, itis necessary to operate the embodiment in the inductive regions. If thevariable inductor is connected to a capacitor in parallel, as shown inFIG. 11, a resonator with tunable resonant frequency can be implemented.The effect of the resistive components is considered in the analysisbelow.

The following equation can then be derived from FIG. 11: $\begin{matrix}{L_{eff} = {L_{1} + \frac{\omega^{2}k^{2}L_{1}L_{2}{C_{2}\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)}}{\left( {1 - {\omega^{2}L_{2}C_{2}}} \right)^{2} + {\omega^{2}{C_{2}}^{2}{r_{2}}^{2}}}}} & (5) \\{\omega = \frac{1}{\sqrt{L_{eff}C_{1}}}} & (6)\end{matrix}$

It is easier to solve the above equations using a graphical method. Asan example, different curves of variable inductance against frequencywith different values of C₂, represented by equation (5) are shown inFIG. 12. The intersecting points correspond to the roots of equation (5)An example of the effective inductance against the values of C₂ is shownin FIG. 13.

The corresponding Z₁₁ of the resonator with the same variable inductorand the same value of C₁ is also plotted. This is aligned with FIG. 12and shown in FIG. 14. By comparing both figures, it can be seen that theintersecting points locate at the same frequency, at which the maximumvalues of Z₁₁ of the resonator locate. This is the resonant frequencywhere the inductive component of the variable inductors cancels exactlywith the capacitance, C₁.

By referring to FIG. 14, it can be seen that there are more than oneintersecting point for each set of curves. This implies that more thanone mode of resonance are available with an embodiment of the invention.It can be seen that, in the second mode, the intersecting points locateat the same frequency, at which the second peaks of Z₁₁ of the resonatorlocate. This is the resonant frequency where the inductive component ofthe variable inductors cancels exactly with the capacitance, C/, in thesecond mode of resonance.

As mentioned before, this phenomenon can be explained intuitively byFIG. 6, which shows the representation of an embodiment of the presentinvention using the π model. In FIG. 6 the two LC tanks coupled to eachother by the mutual inductance explain the two inherent resonantfrequencies in the embodiment of the invention. This property can beapplied to an oscillator for a wide-band voltage-controlled oscillator.

In an oscillator, a resonant tank should be combined with an activecircuit, which is used to cancel the resistive loss of the resonanttank. By combining with the active circuit, oscillation will start atthe frequency with the higher quality factor, which requires less energyto start oscillation. By making use of the two inherent resonantfrequencies in embodiments of the present invention, the oscillator canswitch from one mode of oscillation to another. This can be achieved bychanging the values of C2 in the current invention, which adjusts theresonant frequency, as well as, the maximum values of the impedance ineach mode. When C₂ increases beyond a particular value, there is a swapin the maximum value of the impedance. This is illustrated in FIG. 15.

An embodiment of the present invention may be compared with a simple LCtank. In a first comparison, both an embodiment of the current inventionand a simple inductor are connected with a 1p-10pF capacitor and thevalue of the inductance, L₁, in the embodiment of the invention is thesame as the inductance in the simple LC tank. The maximum resonantfrequency of the simple LC tank is 5.6 GHz, whereas the maximum resonantfrequency of the tank with the variable inductor according to anembodiment of the invention is around 19 GHz. Next, the capacitor in thesimple LC tank is reduced by four times to attain a similar resonantfrequency to the resonator comprised of the embodiment of the presentinvention. It can be seen that, although the simple LC tank can achieveresonant frequency close to that formed by an embodiment of the presentinvention, the magnitude of the simple resonant tank is still only 70%of the tank with the variable inductor. The increase in the magnitude isdue to coupling of the coils in transformer. Since the present inventionconsists of coupled resonators, the invented variable inductor has aquality factor being 1+k times larger than that of a simple LC tank. At11.2 GHz, the Q of the tank with the variable inductor is 11.4, whereasthe Q of the tank with the simple LC tank is only 7.4, which is only 65%of the variable inductor. Besides the increase in the magnitude, theresonator according to an embodiment of the invention also has two modesof resonance, compared to the single mode of resonance in the simple LCtank.

An example of a voltage-controlled oscillator is designed using anembodiment of the present invention is shown in FIGS. 16 and 17. Thetransistors in the oscillator are the active circuit called thenegative-g_(m) cell, which is used to cancel the resistive components ofthe resonator. The VCO is designed with a differential configuration.This requires a four-port transformer. This is feasible with only simplelayout by using symmetrical and center-tapped transformer.

The simulation results are shown in FIG. 18. Simulated oscillationfrequency, phase noise and the power consumption against the value ofC₂, are shown in the figure. The oscillation frequency decreases whenthe value of C₂ increases. The change in C₂ is achieved by a 4-bitswitched capacitor array. As mentioned before, there should be two modesof resonance. This can be verified by the large increase in frequencywhen the value of C₂ is tuned from 5 pF to 8 pF. The results aresummarized in Table 1 below. Due to the tuning in a single mode and theswitching of resonant frequency, the oscillator can be tuned from 5.8GHz to 17 GHz (98%). TABLE 1 Summary of the simulation results and thecomparison with simple LC tank Simple LC Simple LC Variable tank w/sametank w/large Structure inductor power power Process TSMC 0.18 μm Supplyvoltage N 1 Frequency/GHz 5.8-17  4.2-4.5 1.9-3.6 Tuning range 98% 7%60% Amplitude(single-ended)/V 0.5-0.9 0.26-0.56 0.5-1.6 Power/mW 3.1-4.03.8-3.9 17.7-19.8 Phase nosie/dBc@10 MHz −126-−136 −128-−133 −143-−137

The tuning range of this design is much larger compared to thatachievable with existing state-of-the-art designs, which is usuallylimited to less than 20%. In order to achieve such a wide tuning range,only a ring oscillator can be used, but it has much inferior performancein terms of frequency, phase noise, and power consumption.

Comparison with VCOs using simple LC tanks is also implemented insimulation. The performance of the VCOs is shown in FIG. 19 andsummarized in Table 1. With the similar power consumption, the tuningrange for the simple LC tank is only 7%. By increasing the powerconsumption, the tuning range can be increased to 60%.

Three testing setups were designed to demonstrate the characteristics ofembodiments of the invention. They are:

-   -   1. Testing setup using coupled microstrip lines.    -   2. Testing setup using on-chip transformer and off-chip        capacitor.    -   3. Fabrication of a CMOS VCO using on-chip transformer and        on-chip capacitors.

The purpose of the first testing setup, as shown in FIG. 20, is todemonstrate the functionality of embodiments of the invention byoff-chip components. The lumped element model of the coupled microstriplines is shown in FIG. 21. By changing the values of C₂, the equivalentinductance of the testing setup is adjusted, which is the same as in thecurrent invention.

In this setup, a pair of coupled microstrip lines and shunt capacitorsare used to synthesize two coupled resonators with two differentresonant frequencies. The two microstrip lines are shorted to ground. Aterminal of one of the microstrip lines is soldered to a SMA connectorfor connection with testing equipments.

A network analyzer, 8720ES, is used to measure the S-parameters of theembodiment of the invention when the capacitor is changed from 0.47 pFto 1.5 pF. S₁₁ is then converted to Z₁₁. The plot of the measured Z₁₁and the corresponding plot of the equivalent inductance againstfrequency with different values of C₂ are shown in FIG. 22.

The purpose of the second testing setup, shown in FIG. 23, is todemonstrate the utility of an embodiment of the present invention usingan on-chip transformer. Since an on-chip variable capacitor is notavailable, the secondary coil of the on-chip transformer is connected toa capacitor using bondwire. The turn ratio of the on-chip transformer is1:2. The capacitor used is an off-chip surface mount capacitor. Bychanging the off-chip capacitor, the equivalent inductance of thetesting setup is adjusted, which is the same as in an embodiment of thecurrent invention. Silver paint is used to attach the surface mountcapacitor on a pad in the PCB. The same pad is connected to the on-chiptransformer using bondwire.

A network analyzer, 8720ES, is used to measure the S-parameters of theinvention when the capacitor is changed from 0.47 pF to 3.3 pF. S₁₁ isthen converted to Z₁₁. The Smith chart of the measured S₁₁ and thecorresponding plot of the equivalent inductance against frequency withdifferent values of off-chip capacitor are shown in FIGS. 24 and 25respectively.

It is important to notice that the self-resonant frequency ofsurface-mount capacitor is around 6 GHz. The performance of theembodiment of the invention using this setup is, therefore, limited tofrequency around 6 GHz. In the measurement results, the data points atfrequency larger than 6 GHz is not reliable. Yet, the data points below6 GHz already demonstrate the change of inductance with the off-chipcapacitors.

The third experiment is done through a VCO utilizing the presentinvention, which is fabricated using TSMC 0.18 μm CMOS technology. Theresonator of the VCO composes of an on-chip 4-port transformer andon-chip switched capacitor array. By switching the SCA, the outputfrequency of the VCO can be adjusted. Its schematic is similar to theone shown in FIG. 16 and its die photo with DC bias connected usingbondwires is shown in FIG. 26. On-chip measurement was done usinghigh-speed SGS. It is found that by increasing the capacitance to 5 pFat the secondary coil using SCA, the output frequency can be changedfrom 6.71 GHz to 10.49 GHz. In conventional design, increasing thecapacitance of a resonator can only reduce the oscillation frequency. Inthis design, which utilizes the present invention, increasing thecapacitance to a particular value switches the oscillation from thefirst mode to the second one. The frequency spectrum and the phase noiseplots at the output of the VCO are shown in FIG. 27 and FIG. 28. Theperformance of the VCO is summarized in Table 2. This fabricated VCOverifies the existence of a second oscillation mode inherent in thepresent invention and successfully demonstrates the switching mechanismof the different oscillation modes. TABLE 2 Summary of the performanceof the fabricated VCO Frequency/ Output Phase GHz C₂/pF power/dBm noiseV_(supply)/V Power/mW 6.69 0 −11.76 −131.55 1 3.30 10.52 3.366 −20.61−114.66 1 4.17

It will thus be seen that in preferred embodiments of the invention,together with its own parasitic capacitance the primary coil willresonate at different frequencies which are determined by the value ofthe capacitance at the secondary coil. By connecting another varactor atthe primary coil, the frequency tuning range can be further extended tobe much larger than that can be achieved with existing solutions withvariable capacitors. It has also been shown by theory, simulation, andexperiments that there exist two different resonant modes associatedwith the proposed variable inductor. The tuning range of the inventioncan be greatly increased by combining the two modes. Since embodimentsof the invention are only composed of passive components, powerconsumption is low.

Resonators with very wide tuning range can then be implemented withembodiments of the invention and used in different applications. As anexample, conventional LC oscillators have limited frequency tuning rangeand limited performance in phase noise and power consumption, inparticular at high frequencies and low supply voltage, mainly because ofthe varactor requirement. With the proposed variable inductor, thecapacitor can be fixed and be small so that all the parameters includingfrequency tuning range, phase noise, and power consumption, can begreatly improved. The invention has been applied to a VCO to achievewide frequency tuning range and high performance that are not achievablewith existing technologies.

1. A variable inductor comprising a transformer having a primary coiland a secondary coil, wherein a variable capacitance is provided inparallel with said secondary coil.
 2. The variable inductor as claimedin claim 1 wherein said variable capacitance comprises a varactor. 3.The variable inductor as claimed in claim 1 wherein said variablecapacitance comprises a switched capacitor array.
 4. The variableinductor as claimed in claim 1 wherein a capacitance is provided inparallel with the primary coil.
 5. The variable inductor as claimed inclaim 4 wherein said capacitance in parallel to said primary coilcomprises a fixed capacitor.
 6. The variable inductor as claimed inclaim 4 wherein said capacitance in parallel to said primary coilcomprises parasitic capacitance of said primary coil.
 7. The variableinductor as claimed in claim 4 wherein said capacitance in parallel tosaid primary coil comprises another variable capacitance.
 8. Thevariable inductor as claimed in claim 1 wherein said primary coil andsaid secondary coil are coupled together by a mutual inductance.
 9. Avoltage controlled oscillator including a variable inductor comprising atransformer having a primary coil and a secondary coil, wherein avariable capacitance is provided in parallel to said secondary coil. 10.The voltage controlled oscillator as claimed in claim 9 wherein saidvariable capacitance comprises a varactor.
 11. The voltage controlledoscillator as claimed in claim 9 wherein said variable capacitancecomprises a switched capacitor array.
 12. The voltage controlledoscillator as claimed in claim 9 wherein a capacitance is provided inparallel with the primary coil.
 13. The voltage controlled oscillator asclaimed in claim 12 wherein said capacitance in parallel to said primarycoil comprises a fixed capacitor.
 14. The voltage controlled oscillatoras claimed in claim 12 wherein said capacitance in parallel to saidprimary coil comprises parasitic capacitance of said primary coil. 15.The voltage controlled oscillator as claimed in claim 12 wherein saidcapacitance in parallel to said primary coil comprises another variablecapacitance.
 16. The voltage controlled oscillator as claimed in claim 9wherein said primary coil and said secondary coil are coupled togetherby a mutual inductance.
 17. The voltage controlled oscillator as claimedin claim 9 wherein a second negative gm cell is connected to thesecondary coil.
 18. The voltage controlled oscillator as claimed inclaim 9 wherein a coupling enhancement circuit is connected to thesecondary coil.
 19. The voltage controlled oscillator as claimed inclaim 9 wherein transformer feedback from a drain of a transistor to asource of the transistor is used to enhance the oscillation.
 20. Thevoltage controlled oscillator as claimed in claim 9 wherein transformerfeedback from a gate of a transistor to a source of the transistor isused to enhance the oscillation.